$(10$ points$)$ The table below describes a Turing machine. Run machine on the input string $000000.$

$($Show the sequence of configurations.$)$ You may assume that qA is the accept state and qR is the reject

state.

$0$ X B

q$0($q$1,$ B$,$ R$)$

q$1($q$2,$ X$,$ R$)$ RIGHT ACCEPT

q$2($q$3,0,$ R$)$ RIGHT $($q$4,$ B$,$ L$)$

q$3($q$2,$ X$,$ R$)$ RIGHT $$

q$4$ LEFT LEFT $($q$1,$ B$,$ R$)$

$3.(10$ points$)$ Give the formal definition, $($Q$,,,$ $,$ q$0,$ F $),$ of a PDA that recognizes the following CFG$.$

Use the construction from the lecture.

T $$ V aV

V $$ cT $|$ bb

$2.(10$ points$)$ The table below describes a Turing machine. Run machine on the input string $000000.($Show the sequence of configurations.$)$ You may assume that $\backslash ($ q$\_\{$A$\}\backslash )$ is the accept state and $\backslash ($ q$\_\{$R$\}\backslash )$ is the reject state.